Question

Tom, Dick and Harry are three friends. They keep saying their names at regular intervals. While Tom says his name every 12 seconds, Dick and Harry say their names every 30 and 42 seconds respectively. If they start by saying their names together, then when will they all say their names in unison again?

• A. 4 hours
• B. 5 hours
• C. 6 hours
• D. 7 hours

Answer 1

The correct option is D

7 hours

Tom, Dick and Harry will say their names out in unison at a time gap which is equal to a common multiple of 12, 30 and 42

$12=2\times 2\times 3$

$30=2\times 3\times 5$

$42=2\times 3\times 7$

LCM = $2\times 2\times 3\times 5\times 7=420\text{seconds}$ = $\frac{420}{60}$ = $7\text{minutes}$

$\therefore$ After 7 minutes, they all will say their names together.